Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
How to Use This Page
1. Attempt every exercise question on your own first — cover the answer, write your solution on paper, then compare. 2. Focus on the method, not just the final number. The step-by-step working shows you how to think. 3. Pay special attention to "Common Mistakes" — these are the exact errors examiners mark most often. 4. Use the Exam Checklist before your test to make sure you have revised every key formula and concept. 5. Numerical examples in code blocks show SI units at every step — always include units in your exam answers.
Key Concepts (Quick Recap)
Equations of Uniformly Accelerated Motion
| Equation | Formula | Use When You Know |
|---|---|---|
| First | v = u + at | u, a, t → v |
| Second | s = ut + ½at² | u, a, t → s |
| Third | v² = u² + 2as | u, a, s → v (no t needed) |
- u = initial velocity (m/s), v = final velocity (m/s), a = acceleration (m/s²), s = displacement (m), t = time (s)
Projectile Motion (launched at angle θ with speed u)
| Quantity | Formula |
|---|---|
| Horizontal component | uₓ = u cos θ |
| Vertical component | u_y = u sin θ |
| Time of flight | T = 2u sin θ / g |
| Maximum height | H = u² sin²θ / 2g |
| Range | R = u² sin 2θ / g |
Relative Velocity
- v_AB = v_A − v_B (along same line)
- For 2D: v_AB = v_A − v_B (vector subtraction)
Free Fall
- Acceleration = g = 9.8 m/s² (downward), air resistance neglected
- Upward thrown: a = −g (deceleration phase)
Important Definitions
| Term | Definition |
|---|---|
| Displacement | Shortest distance from initial to final position (vector) |
| Distance | Total path length travelled (scalar) |
| Speed | Rate of change of distance (scalar) |
| Velocity | Rate of change of displacement (vector) |
| Acceleration | Rate of change of velocity (vector) |
I. Choose the Best Answer (MCQs)
II. Fill in the Blanks
1. The slope of the displacement-time graph gives ________. Velocity 2. The slope of the velocity-time graph gives ________. Acceleration 3. A body dropped from rest falls through 4.9 m in the first ________ second(s) (g = 9.8 m/s²). One 4. For a projectile, the horizontal component of velocity remains ________. Constant 5. The path of a projectile is a ________. Parabola 6. If v_A = 10 m/s east and v_B = 6 m/s east, then v_AB = ________ m/s east. 4 7. The SI unit of acceleration is ________. m/s² 8. When a body is thrown upward, its acceleration is ________ (positive/negative/zero). Negative 9. The range of a projectile is maximum when the angle of projection is ________. 45° 10. In uniform circular motion, speed is constant but velocity ________. Changes 11. Displacement is a ________ quantity (scalar/vector). Vector 12. The distance covered in the nth second formula s_n = u + a/2(2n − 1) is derived from the ________ equation of motion. Second
III. True or False (with corrections)
1. Distance is always equal to displacement.
- False. Displacement is the shortest path from start to end; distance is the total path length and is always ≥ displacement.
2. A body can have zero velocity but non-zero acceleration.
- True. Example: at the highest point of a vertically thrown ball, v = 0 but a = g downward.
3. The horizontal and vertical motions of a projectile are dependent on each other.
- False. They are independent. Horizontal motion has no acceleration; vertical motion has acceleration g downward.
4. Average speed can be less than average velocity.
- False. Average speed ≥ average velocity because distance ≥ |displacement|. Average speed can equal average velocity but can never be less.
5. A freely falling body has constant acceleration g.
- True. Near Earth's surface, air resistance neglected, g ≈ 9.8 m/s² acts downward constantly.
IV. Match the Following
| Column A | Column B |
|---|---|
| 1. Slope of s-t graph | (c) Velocity |
| 2. Area under v-t graph | (d) Displacement |
| 3. Slope of v-t graph | (a) Acceleration |
| 4. Projectile path | (e) Parabola |
| 5. s_n (displacement in nth second) | (f) u + a/2(2n − 1) |
| 6. Maximum range condition | (b) θ = 45° |
V. Answer Briefly (2-mark Questions)
VI. Answer in Detail (5-mark Questions with Numerical Examples)
Common Mistakes to Avoid
| 1. Confusing distance and displacement — distance is always ≥ | displacement | ; they are equal only for straight-line motion in one direction without reversal. |
|---|
2. Sign errors for deceleration — when a body decelerates, assign a = −g or a = negative. Using positive acceleration for deceleration produces wrong answers.
3. Forgetting to resolve velocity into components in projectile problems — always write uₓ = u cos θ and u_y = u sin θ before proceeding.
4. Using v² = u² + 2as without checking sign conventions — if upward is positive, g must be taken as −9.8 or −10 m/s².
5. Mixing up sin θ and cos θ — sin θ gives the vertical component, cos θ the horizontal component. At 45° they are equal; at other angles they differ.
6. Assuming relative velocity is always the sum of speeds — it is the sum only when objects move in opposite directions along the same line. Use vector subtraction in general.
7. Not converting units — speeds in km/h must be converted to m/s (multiply by 5/18) before using in equations of motion.
8. Ignoring air resistance assumption — all projectile formulas assume air resistance is negligible. In exam answers, state this assumption.
Exam Checklist
- [ ] Can write and explain all three equations of motion
- [ ] Can derive equations of motion from calculus (integration of a = dv/dt)
- [ ] Know projectile formulas: T, H, R and their derivations
- [ ] Can resolve velocity into horizontal and vertical components
- [ ] Understand relative velocity formula and sign conventions
- [ ] Can solve free-fall problems (dropped, thrown upward)
- [ ] Know that s-t graph slope = velocity, v-t graph slope = acceleration
- [ ] Can calculate displacement from v-t graph (area)
- [ ] Remember distance in nth second: s_n = u + a/2(2n − 1)
- [ ] Can convert km/h to m/s and apply correct sign conventions throughout